The increasing size and complexity of integrated circuits has lead to the development of advanced algorithms and techniques for circuit simulation. The majority of circuit simulators rely on the Newton-Raphson algorithm for the solution of nonlinear equations that arise from the circuit description. Unfortunately, a good estimate of the root to be found is needed for the algorithm to converge. The convergence rate of the algorithm is quadratic once the method gets "close enough" to the solution, but before reaching this point the method may follow a complex route through unrealistic values of the circuit variables, leading eventually to divergence. Simulations performed with SPICE on several test circuits reveal that during the first iterations of the Newton-Raphson algorithm internal node voltages exceed the power supply voltage of several orders of magnitudes even for simple circuits. A new simulation program called MUSIC (Multilevel Simulator for Integrated Circuits) has been developed to overcome these drawbacks. In MUSIC the circuit to be simulated is decomposed in subcircuits, which may contain instances of other subcircuits up to any nesting level. Subcircuits are then simulated independently with a multilevel Newton algorithm permitting to reduce both the large oscillations that circuit variables undergo during the simulation process and the number of iterations necessary for the circuit to converge. The novel feature of this multilevel algorithm is the propagation of the already calculated terminal voltages, which become known after a subcircuit has converged, to the subcircuits connected to same terminals. In this way the information regarding node voltages is propagated through the network without constraining conditions that do not have physical counterpart. Simulations performed on chains of inverters and a 4-bit full adder evidence how MUSIC is able to improve the convergence rate and to reduce the intermediate voltage spikes.